1. Field of the Invention
The present invention relates to an orthogonal frequency division multiplexing (OFDM) receiver, and more particularly, to a coarse frequency offset estimator in an OFDM receiver, and a method of estimating a coarse frequency offset.
2. Description of the Related Art
FIG. 1 is a block diagram showing the structure of a conventional OFDM receiver. Referring to FIG. 1, the conventional OFDM receiver includes an OFDM demodulator 10 and a coarse frequency offset estimator 12. The OFDM demodulator 10 includes a radio frequency (RF) receiver 101, an analog-to-digital converter (ADC) 102, an in-phase/quadrature (I/Q) separator 103, a frequency corrector 104, a fast Fourier transformer (FFT) 105, and a Viterbi decoder 106. The coarse frequency offset estimator 12 includes a register 121, a complex data multiplier 122, an inverse fast Fourier transformer (IFFT) 123, a maximum value detector 124, a counter 125, and a reference symbol generator 126.
In the operation of the receiver having such a configuration, first, the RF receiver 101. receives an RF wave and outputs an RF signal. The ADC 102 quantizes the RF signal. The I/Q separator 103 separates an in-phase (I) component and a quadrature (Q) component from the quantized RF signal. The frequency corrector 104 performs frequency-correcting. The FFT 105 receives a frequency-corrected signal and performs Fourier-transforming of the frequency-corrected signal, thereby performing demodulation. The Viterbi decoder 106 decodes a demodulated signal.
Meanwhile, the demodulated signal is stored in the register 121 of the coarse frequency offset estimator 12, and is output as a received signal X. A reference symbol which is output by the reference symbol generator 126 is represented by Z. When a received symbol has a frame synchronization offset of xcfx89, and frequency offset does not exist, if the k-th sub-carriers of the received symbol X and the reference symbol Z are Xk and Zk, respectively, Xk and Zk have a relationship as Xk=Zkexe2x88x92J2xcfx80xcfx89|N. The complex data multiplier 122 multiplies the conjugate value of Xk by the conjugate value of Zk. The signal output from the complex data multiplier 122 is inversely Fourier-transformed by the IFFT 123, and the following signal hn is output:                                                                         h                n                            =                              xe2x80x83                            ⁢                              IFFT                ⁢                                  {                                      XZ                    *                                    }                                                                                                        =                              xe2x80x83                            ⁢                                                1                  /                  N                                ⁢                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                            X                      k                                        ⁢                                          Z                      k                      *                                        ⁢                                          ⅇ                                              j2π                        ⁢                                                  xe2x80x83                                                ⁢                                                  kn                          /                          N                                                                                                                                                                                            =                              xe2x80x83                            ⁢                                                1                  /                  N                                ⁢                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                            Z                      k                                        ⁢                                          ⅇ                                                                        -                          j                                                ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                        k                        ⁢                                                  xe2x80x83                                                ⁢                                                  ω                          /                          N                                                                                      ⁢                                          Z                      k                      *                                        ⁢                                          ⅇ                                              j                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                  kn                          /                          N                                                                                                                                                                                            =                              xe2x80x83                            ⁢                                                1                  /                  N                                ⁢                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                                                    "LeftBracketingBar"                                                  Z                          k                                                "RightBracketingBar"                                            2                                        ⁢                                          ⅇ                                              j                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                                              k                            ⁡                                                          (                                                              n                                -                                ω                                                            )                                                                                /                          N                                                                                                                                                                                            =                              xe2x80x83                            ⁢                              δ                ⁡                                  (                                      n                    -                    ω                                    )                                                                                        (        1        )            
A received symbol Xk having an integer multiple xcex94fi of a frequency offset with respect to a transmitted symbol Zk can be expressed as Zkxe2x88x92xcex94fiexe2x88x92J2xcfx80kxcfx89|N, so that Equation 1 can be expressed as the following Equation 2:                                                                         h                n                            =                              IFFT                ⁢                                  {                                      XZ                    *                                    }                                                                                                        =                                                1                  /                  N                                ⁢                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                            X                      k                                        ⁢                                          Z                      k                      *                                        ⁢                                          ⅇ                                              j                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                  kn                          /                          N                                                                                                                                                                                            =                                                1                  /                  N                                ⁢                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                            Z                                              k                        -                                                  Δ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      f                            i                                                                                              *                                        ⁢                                          ⅇ                                                                        -                          j2π                                                ⁢                                                  xe2x80x83                                                ⁢                        k                        ⁢                                                  xe2x80x83                                                ⁢                                                  ω                          /                          N                                                                                      ⁢                                          Z                      k                      *                                        ⁢                                          ⅇ                                              j2π                        ⁢                                                  xe2x80x83                                                ⁢                                                  kn                          /                          N                                                                                                                                                                            (        2        )            
The result of Equation 2 is the same as a process for obtaining the convolution of two signals in the time domain, and the result value hn is a channel impulse response (CIR). As described above, an OFDM system which has reference symbol in a frequency domain can obtain the CIR using a received symbol. Here, because the reference symbol Z consists of a pseudo noise (PN) sequence, maximum peak value exists only if frequency offset xcex94fi, is zero, and if otherwise noisy peaks with small value are gained. Using such a relationship, the coarse frequency offset estimator 12 shifts a received symbol with respect to xcex94fi, and the maximum value detector 124 detects a maximum peak value according to Equation 2. The counter 125 obtains a shift amount xcex94fi in which the maximum peak value is generated. The shift amount xcex94fi becomes an offset value Fo which is an integral multiple of a frequency offset intended to be detected, which establishes a relationship expressed as the following Equation 3:                               F          o                =                                                                                                                        max                                                                                                                                                                                                                                               Δ                  ⁢                                      xe2x80x83                                    ⁢                                      f                    i                                                                                ⁢                      {                          max              ⁢                              xe2x80x83                            ⁢                              amp                ⁡                                  [                                      IFFT                    ⁢                                          {                                                                        X                          R                                                ⁢                        Z                                            }                                                        ]                                                      }                                              (        3        )            
wherein Z denotes a reference symbol, and XR is expressed as a symbol X((k+xcex94fi))N, obtained by shifting an individual sub-carrier Xk of a received symbol X by xcex94fi in the frequency domain.
According to this coarse frequency offset estimation method, a conventional OFDM receiver as described above can theoretically and practically estimate an almost exact frequency offset in all cases regardless of a channel environment or a frame synchronization error. However, this method has significantly many calculation processes. Thus, a very complicated inverse fast Fourier transformation (IFFT) module is required to estimate an accurate frequency offset within a predetermined short period of time. Also, a long response time causes an excessive time delay.
To solve the problem, another conventional coarse frequency offset estimation method is disclosed. According to the method, first, to find out the influence of a frequency offset on the received symbol, fk and foff are defined. Here, fk denotes the frequency of a k-th sub-carrier, and foff denotes an actual frequency offset. The frequency offset is expressed as a multiple of a subcarrier frequency interspacing. Generally, the frequency offset includes an offset expressed as an integral multiple of the subcarrier frequency interspacing, and an offset expressed as a prime multiple thereof, and the multiples are individually processed. Thus, each term in: fk+foff can be defined as the following Equation 4:                                                                         f                k                            =                              k                                  T                  s                                                                                                                        f                off                            =                                                Δ                  ⁢                                      xe2x80x83                                    ⁢                  f                  ⁢                                      xe2x80x83                                    ⁢                                      1                                          T                      s                                                                      =                                                      (                                                                  Δ                        ⁢                                                  xe2x80x83                                                ⁢                                                  f                          i                                                                    +                                              Δ                        ⁢                                                  xe2x80x83                                                ⁢                                                  f                          f                                                                                      )                                    ⁢                                      1                                          T                      s                                                                                                                              (        4        )            
wherein xcex94f denotes the frequency offset of a subcarrier expressed by a multiple of a subcarrier frequency interspacing. Also, xcex94f is expressed as the sum of an integer number xcex94fi and a floating number xcex94ff which satisfies a condition xe2x88x92xc2xd less than xcex94ff less than xc2xd. Under this condition, a received symbol of an n-th symbol is expressed as the following Equation. However, for convenience of the development of the following Equation 5, it is assumed that no noise exists.                                                                                           r                  n                                ⁡                                  (                  m                  )                                            =                              xe2x80x83                            ⁢                                                ∑                                      k                    =                    0                                                        N                    -                    1                                                  ⁢                                                      C                                          n                      ,                      k                                                        ⁢                                      ⅇ                                          j                      ⁢                                              xe2x80x83                                            ⁢                      2                      ⁢                                              π                        ⁡                                                  [                                                                                    k                                                              T                                s                                                                                      +                                                                                          (                                                                                                      Δ                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                                                          f                                      i                                                                                                        +                                                                      Δ                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                                                          f                                      f                                                                                                                                      )                                                            ⁢                                                              1                                                                  T                                  s                                                                                                                                              ]                                                                    ⁢                                                                        T                          s                                                N                                            ⁢                      m                                                                                                                                              =                              xe2x80x83                            ⁢                                                ∑                                      k                    =                    0                                                        N                    -                    1                                                  ⁢                                                      C                                          n                      ,                      k                                                        ⁢                                      ⅇ                                          j                      ⁢                                              xe2x80x83                                            ⁢                      2                      ⁢                                              π                        [                                                                              (                                                          k                              +                                                              Δ                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  f                                  i                                                                                            +                                                              Δ                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  f                                  f                                                                                                                      )                                                    ⁢                                                      m                            /                            N                                                                                                                                                                                                      (        5        )            
wherein Cn,k denotes a k-th sub-carrier of an n-th symbol in a frequency domain, and N denotes the number of OFDM sub-carriers.
Meanwhile, when an integral multiple of a frequency offset xcex94fi among frequency offsets is zero, a demodulated signal Ĉxe2x80x2n,p is expressed as the following Equation 6:                                                                                           C                  ^                                                  n                  ,                  p                                xe2x80x2                            =                              xe2x80x83                            ⁢                                                1                  N                                ⁢                                                      ∑                                          m                      =                      0                                                              N                      -                      1                                                        ⁢                                                                                    r                        n                                            ⁡                                              (                        m                        )                                                              ⁢                                          ⅇ                                                                        -                          j                                                ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                        m                        ⁢                                                  xe2x80x83                                                ⁢                                                  p                          /                          N                                                                                                                                                                                            =                              xe2x80x83                            ⁢                                                1                  N                                ⁢                                                      ∑                                          m                      =                      0                                                              N                      -                      1                                                        ⁢                                                            ∑                                              k                        =                        0                                                                    N                        -                        1                                                              ⁢                                                                  C                                                  n                          ,                          k                                                                    ⁢                                              ⅇ                                                  j                          ⁢                                                      xe2x80x83                                                    ⁢                          2                          ⁢                                                      π                            ⁡                                                          (                                                              k                                +                                                                  Δ                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      f                                    i                                                                                                                              )                                                                                ⁢                                                      m                            N                                                                                              ⁢                                              ⅇ                                                                              -                            j2π                                                    ⁢                                                      xe2x80x83                                                    ⁢                          m                          ⁢                                                      xe2x80x83                                                    ⁢                                                      p                            /                            N                                                                                                                                                                                                                      =                              xe2x80x83                            ⁢                                                1                  N                                ⁢                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                            C                                              n                        ,                        k                                                              ⁢                                                                  ∑                                                  m                          =                          0                                                                          N                          -                          1                                                                    ⁢                                              ⅇ                                                                              j2π                            ⁡                                                          (                                                              k                                +                                                                  Δ                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      f                                    i                                                                                                  -                                p                                                            )                                                                                ⁢                                                      m                            N                                                                                                                                                                                                                      =                              xe2x80x83                            ⁢                                                1                  N                                ⁢                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                            C                                              n                        ,                        k                                                              ⁢                                          {                                                                        ⅇ                                                      jπ                            ⁡                                                          (                                                              p                                -                                k                                -                                                                  Δ                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      f                                    f                                                                                                                              )                                                                                                      ⁢                                                                              sin                            ⁡                                                          (                                                              π                                ⁡                                                                  (                                                                      p                                    -                                    k                                    -                                                                          Δ                                      ⁢                                                                              xe2x80x83                                                                            ⁢                                                                              f                                        f                                                                                                                                              )                                                                                            )                                                                                                            N                            ⁢                                                          xe2x80x83                                                        ⁢                                                          sin                              ⁡                                                              (                                                                  π                                  /                                                                      N                                    ⁡                                                                          (                                                                              p                                        -                                        k                                        -                                                                                  Δ                                          ⁢                                                                                      xe2x80x83                                                                                    ⁢                                                                                      f                                            f                                                                                                                                                              )                                                                                                                                      )                                                                                                                                                        }                                                                                                                              (        6        )            
As shown in the last line of Equation 6, the demodulated signal Ĉxe2x80x2n,p is calculated depending on an integer of k. Thus, if a frequency offset xcex94ff of a prime multiple is zero, the demodulated signal Ĉxe2x80x2n,p having peaks is output only at a frequency where k is equal to p, and a demodulated signal Ĉxe2x80x2n,p having a zero peak is output at other frequencies. That is, the orthogonality between frequencies is kept. However, if the frequency offset xcex94ff is not zero, the peak of the demodulated signal Ĉxe2x80x2n,p is reduced even at a frequency where k is equal to p, and the demodulated signal Ĉxe2x80x2n,p having peaks other than a zero peak is output at other frequencies. Such a phenomenon causes interference between sub-carriers, thus becoming a factor of interchannel interference (ICI). The demodulated signal Ĉxe2x80x2n,p is obtained from the received signal of Equation 5 as the following Equation 7:                                                                                           C                  ^                                                  n                  ,                  p                                            =                              xe2x80x83                            ⁢                                                1                  N                                ⁢                                                      ∑                                          m                      =                      0                                                              N                      -                      1                                                        ⁢                                                                                    r                        n                                            ⁡                                              (                        m                        )                                                              ⁢                                          ⅇ                                                                        -                          j                                                ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                        m                        ⁢                                                  xe2x80x83                                                ⁢                                                  p                          /                          N                                                                                                                                                                                            =                              xe2x80x83                            ⁢                                                1                  N                                ⁢                                                      ∑                                          m                      =                      0                                                              N                      -                      1                                                        ⁢                                                            ∑                                              k                        =                        0                                                                    N                        -                        1                                                              ⁢                                                                  C                                                  n                          ,                          k                                                                    ⁢                                              ⅇ                                                  j                          ⁢                                                      xe2x80x83                                                    ⁢                          2                          ⁢                          π                          ⁢                                                      xe2x80x83                                                    ⁢                          k                          ⁢                                                      xe2x80x83                                                    ⁢                                                      m                            /                            N                                                                                              ⁢                                              ⅇ                                                                              -                            j2π                                                    ⁢                                                      xe2x80x83                                                    ⁢                                                                                    m                              ⁡                                                              (                                                                  p                                  -                                                                      Δ                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                                                          f                                      i                                                                                                                                      )                                                                                      /                            N                                                                                                                                                                                                                      =                              xe2x80x83                            ⁢                                                C                  ^                                                  n                  ,                                      p                    -                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                                              f                        i                                                                                            xe2x80x2                                                                        (        7        )            
This result shows that when a frequency offset, an integral multiple of a sub-carrier frequency, is xcex94fi, a signal to be demodulated is shifted by xcex94fi and demodulated. Here, Equation 7 includes a discrete Fourier transformation (DFT) process, and shifted demodulation is performed through cyclic shifting.
Therefore, according to the another example of conventional coarse frequency offset estimation method, a correlation value is obtained while cyclic shifting an already-known phase reference symbol and a received signal for a symbol period, and the amount of shift for which the correlation value is maximum is determined to be an integral multiple of a frequency offset. This relationship is expressed as the following Equation 8:                                                                                                               max                                                                                                                                                                                                   d                                      ⁢                  {                                    ∑                              k                =                0                                            N                -                1                                      ⁢                          X              ⁡                              (                                                      (                                                                  (                                                  k                          +                          d                                                )                                            N                                        )                                    ⁢                                                            Z                      *                                        ⁡                                          (                      k                      )                                                                      )                                              }                                    (        8        )            
wherein ((k+d)N) is a symbol indicating a modulo-N addition operation, X(k) denotes a k-th received signal after DFT, and Z(k) denotes a k-th phase reference signal. Also, both X(k) and Z(k) are signals in the frequency domain.
However, this method cannot correct a frequency offset when frame synchronization has not been achieved.
An objective of the present invention is to provide a coarse frequency offset estimator in an orthogonal frequency division multiplexing (OFDM) receiver, by which frequency synchronization is stably performed through a small number of calculations.
Another objective of the present invention is to provide a coarse frequency offset estimating method performed by the device.
Still another objective of the present invention is to provide an OFDM receiver which can perform stable frequency synchronization through a small number of calculations.
Accordingly, to achieve the above first objective, the present invention provides a device for estimating a coarse frequency offset in an orthogonal frequency division multiplexing (OFDM) receiver, the device including: a buffer for receiving demodulated symbol X(k) and cyclic shifting the symbol X(k) by a predetermined shift amount d and outputting shifted symbol X(k+d); a reference symbol generator for generating a reference symbol Z(k); a counter for counting the shift amount of d; a partial correlation for receiving the shifted symbol X(k+d) and the phase reference symbol Z(k) and calculating a partial correlation value       ∑          m      =      0              K      -      1        ⁢      xe2x80x83    ⁢      "LeftBracketingBar"                  ∑                  k          =                      m            ⁢                          xe2x80x83                        ⁢                          (                              N                /                K                            )                                                                          (                              m                +                1                            )                        ⁢                          xe2x80x83                        ⁢                          (                              N                /                K                            )                                -          1                    ⁢              xe2x80x83            ⁢              X        ⁢                  xe2x80x83                ⁢                  (                                    (                                                (                                      k                    +                    d                                    )                                N                            )                        ⁢                          xe2x80x83                        ⁢                          Z              *                        ⁢                          xe2x80x83                        ⁢                          (              k              )                                )                      "RightBracketingBar"  
with respect to K divided bands, wherein a range of shift amount d is between xe2x88x92N/2 and N/2; and a maximum detector for obtaining a shift amount of d by which the partial correlation value is maximum, and outputting the shift amount of d as an estimated coarse frequency offset value.
It is preferable that the number of divided bands, K, is set to be within 2 Toff when a timing synchronization offset which can be covered by frame synchronization is set to be Toff.
To achieve the second objective, the present invention provides a method of estimating a coarse frequency offset in an orthogonal frequency division multiplexing (OFDM) receiver, the method including the steps of: (a) generating a reference symbol Z(k); (b) counting the shift amount of d; (c) receiving the shifted symbol X(k+d) and the phase reference symbol Z(k); (d) calculating a partial correlation value       ∑          m      =      0              K      -      1        ⁢      xe2x80x83    ⁢      "LeftBracketingBar"                  ∑                  k          =                      m            ⁢                          xe2x80x83                        ⁢                          (                              N                /                K                            )                                                                          (                              m                +                1                            )                        ⁢                          xe2x80x83                        ⁢                          (                              N                /                K                            )                                -          1                    ⁢              xe2x80x83            ⁢              X        ⁢                  xe2x80x83                ⁢                  (                                    (                                                (                                      k                    +                    d                                    )                                N                            )                        ⁢                          xe2x80x83                        ⁢                          Z              *                        ⁢                          xe2x80x83                        ⁢                          (              k              )                                )                      "RightBracketingBar"  
with respect to K divided bands, wherein a range of shift amount d is between xe2x88x92N/2 and N/2; and (e) obtaining a shift amount of d by which the partial correlation value is maximum, and outputting the shift amount of d as an estimated coarse frequency offset value.
To achieve the third objective, the present invention provides an orthogonal frequency division multiplexing (OFDM) receiver including: a buffer for receiving demodulated symbol X(k) and cyclic shifting the symbol X(k) by a predetermined shift amount d and outputting shifted symbol X(k+d); a reference symbol generator for generating a reference symbol Z(k); a counter for counting the shift amount of d; a partial correlation for receiving the shifted symbol X(k+d) and the phase reference symbol Z(k) and calculating a partial correlation value       ∑          m      =      0              K      -      1        ⁢      xe2x80x83    ⁢      "LeftBracketingBar"                  ∑                  k          =                      m            ⁢                          xe2x80x83                        ⁢                          (                              N                /                K                            )                                                                          (                              m                +                1                            )                        ⁢                          xe2x80x83                        ⁢                          (                              N                /                K                            )                                -          1                    ⁢              xe2x80x83            ⁢              X        ⁢                  xe2x80x83                ⁢                  (                                    (                                                (                                      k                    +                    d                                    )                                N                            )                        ⁢                          xe2x80x83                        ⁢                          Z              *                        ⁢                          xe2x80x83                        ⁢                          (              k              )                                )                      "RightBracketingBar"  
with respect to K divided bands, wherein a range of shift amount d is between xe2x88x92N/2 and N/2; and a maximum detector for obtaining a shift amount of d by which the partial correlation value is maximum, and outputting the shift amount of d as an estimated coarse frequency offset value.